Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Sin 72 Degrees

    Sin, Cos, Tan, Cot of an Angle
    Function
    Angle (°)

    What is sin 72°?

    Answer

    sin 72° =
    √(10 + 2√5)/4 ≈ 0.9511

    Angle in radians: 72° = 2π/5. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 72°, sin 72°) = ((√5 − 1)/4, √(10 + 2√5)/4)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    sin 72° = cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

    xyOP

    P(cos 72°, sin 72°) ≈ (0.3090, 0.9511)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.9511.

    All four functions of 72°
    FunctionExact valueDecimal
    sin 72°√(10 + 2√5)/4≈ 0.9511
    cos 72°(√5 − 1)/4≈ 0.3090
    tan 72°√(5 + 2√5)≈ 3.0777
    cot 72°√(25 − 10√5)/5≈ 0.3249

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/sin--72Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--72">Sin 72 Degrees: Sine of 72° on the Unit Circle - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Sin 72 Degrees: Sine of 72° on the Unit Circle. sin 72° = √(10 + 2√5)/4 ≈ 0.9511. The sine is the y-coordinate of the point at 72° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--72/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    69°≈ 0.9336
    70°≈ 0.9397
    71°≈ 0.9455
    72°√(10 + 2√5)/4
    73°≈ 0.9563
    74°≈ 0.9613
    75°(√6 + √2)/4
    Recalculate with different values ↑

    FAQ

    What is sin 72°?

    sin 72° = √(10 + 2√5)/4 ≈ 0.9511

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show 0.2538 for sin 72?

    The calculator is in radian mode (RAD): it takes sin 72 as the sine of 72 radians, sin 72 rad ≈ 0.2538. Switch it to degrees (DEG): sin 72° = √(10 + 2√5)/4 ≈ 0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also